You didn't show a picture of the flapper valve...sometimes the rubber in it degrades and flakes off. It could be a mold and a thorough cleaning and disinfectant may be required. Regular use of things like bleach in the tank will eat up the rubber components and ruin them, so you don't want to use in-tank things. It could also be the insides of the hose used to connect the tank to the shutoff at the wall are breaking down.

Looks like that mold/scum thing. We have the same deal. Some toilets "catch" it, others don't, all in the same house. I had pretty good success just spraying everything down with Tilex Mold and Mildew remover and letting it sit for half an hour (after turning off the water and flushing to empty the tank, of course).

Only one of the 3 original toilets in our house caught that black scum thing. the two 3.5 GPF Wellworths didn't have it, the 3.5 GPF Eljer Emblem (terrible high flow flusher btw) had it, was the most used in the house. Never did anything about it except toss it out many years ago for a Drake.